Using multivariate linear regression to estimate permeability from 2D image analysis

The pore system of conventional sandstone reservoirs consists of pore bodies, that constitutes the bulk of the pore space, and pore throats that represent constrictions between pore bodies. The number and size of pore throats control many important rock characteristics, including the ability to transmit fluids (i.e., permeability), and capillary pressure. Compared to 3D images, 2D thin section images can be readily segmented for porosity, and 2D estimates of pore body and pore throat size distributions can be generated at relatively low cost. We illustrate a multivariate linear regression model that uses the measured characteristics of pore bodies and pore throats in thin section to estimate absolute permeability of sandstones. The important characteristics of the pore system that are used for modeling permeability include mean pore body size, standard deviation of pore body size, 2D estimate of specific surface area, mean pore throat size, and the average pore body coordination number (number of pore throats connected to each pore body). A fractal dimension correction was applied to the estimates of specific surface area to remove the influence of image magnification on that parameter. Results of image analysis were calibrated using brine permeability and NMR-T2 distribution measurements on companion core plugs.